Combining Functions MCC9-12.F.BF.1b Combine standard function types using arithmetic operations.

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Presentation transcript:

Combining Functions MCC9-12.F.BF.1b Combine standard function types using arithmetic operations.

Adding Linear Functions f(x) + g(x) If f(x)= 3x - 4 and g(x) = -2x + 6, find f(x) + g(x). (3x – 4) + (-2x + 6) OR 3x – x +6 1x + 2 So, f(x) + g(x) = 1x + 2

Adding Linear Functions If f(x) = 7x + 3 and g(x) = 6x – 4, find f(x) + g(x).

Subtracting Linear Functions f(x) - g(x) If f(x) = 4x -29 and g(x)= 2x – 18, find f(x) – g(x). (4x – 29) – (2x -18) change – to + the opposite. (4x – 29) + (-2x +18) 4x – x x - 11 So, f(x) – g(x) = 2x – 11

Subtracting Linear Functions If f(x) = -3x + 15 and g(x) = -4x -17, find f(x) – g(x).

Multiplying Linear Functions f(x) · g(x) If f(x) = 3x and g(x) = 2x -17, find f(x)·g(x). (3x)(2x-17) = 3x(2x) – 3x(17) = 6x 2 – 51 So, f(x) · g(x) = 6x 2 – 51

Multiplying Linear Functions If f(x) = x - 13 and g(x) = -5x, find f(x)·g(x).

Dividing Linear Functions f(x) / g(x) If f(x) = 6x and g(x) = 2x, find f(x)/g(x). 6x/2x = 3 So, f(x) / g(x) = 3

Dividing Linear Functions If f(x) = x + 5 and g(x) = 2x, find f(x)/g(x).

Adding exponential functions f(x) + g(x) If f(x) = 2 x and g(x) = 2 x, find f(x) + g(x). 2 x + 2 x = 2(2 x )

Adding exponential functions If f(x) = 2(4 x ) and g(x) = 4 x, find f(x) + g(x)

Subtracting exponential functions f(x) – g(x) If f(x) = 5(8 x ) and g(x) = 2(8 x ), find f(x) – g(x). 5(8 x ) – 2(8 x ) = 3(8 x ) So f(x) – g(x) = 3(8 x )

Subtracting exponential functions If f(x) = 4(6 x ) and g(x) = 7(6 x ), find f(x) – g(x).

Multiplying exponential functions If f(x) = 5 2x and g(x) = 5 x, then find f(x)·g(x). 5 2x · 5 x = 5 2x + x = 5 3x When multiplying exponential functions, bases must be the same. You add the exponents. So f(x) · g(x) = 5 3x

Multiplying exponential functions If f(x) = 8(9) x and g(x) = 1/2(9) -2x, find f(x) · g(x).

Dividing Exponential Functions f(x)/g(x) If f(x) = 8(2 6x ) and g(x) = 4(2 3x ), find f(x)/g(x). 8(2 6x ) = 2(2 3x ) 4(2 3x )

Dividing Exponential Functions If f(x) = 8(9 4x ) and g(x) = 2(9 -3x ), find f(x)/g(x).